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NEW YORK — Stocks had their worst day of trading since the Sept. 11, 2001, terrorist attacks Tuesday, hurtling the Dow Jones industrials down more than 400 points on a worldwide tide of concern that the U.S. and Chinese economies are stumbling and that share prices have become overinflated. The steepness of the market’s drop, as well as its global breadth, signaled a possible correction after a long period of stable and steadily rising stock markets that had not been shaken by such a volatile day of trading in several years. A 9 percent slide in Chinese stocks, which came a day after investors sent Shanghai’s benchmark index to a record high close, set the tone for U.S. trading. The Dow began the day falling sharply, and the decline accelerated throughout the course of the session before stocks took a huge plunge in late afternoon as computer-driven sell programs kicked in, and also as a computer glitch caused a delay in the recording of a large number of trades. The Dow fell 546.02, or 4.3 percent, to 12,086.06 before recovering some ground in the last hour of trading to close down 416.02, or 3.29 percent, at 12,216.24, leaving it in negative territory for the year. Because the worst of the plunge took place after 2:30 p.m., the New York Stock Exchange’s trading limits, designed to halt such precipitous moves, were not activated. The decline was the Dow’s worst since Sept. 17, 2001, the first trading day after the terror attacks, when the blue chips closed down 684.81, or 7.13 percent. The drop hit every sector across the market. Riskier issues such as small-cap and technology stocks suffered some of the biggest declines, but big industrial companies, those that are often hurt the most in an economic downturn, also were pummeled, with raw materials producers among the hardest hit. But analysts who have been expecting a pullback after a huge rally that began last October and sent the Dow to a series of record highs, were unfazed by Tuesday’s drop. ‘‘This corrective consolidation phase isn’t just going to be one day, but we don’t believe this is going to be a bear market,’’ said Bob Doll, BlackRock’s global chief investment officer of equities. Some investors also tried to put Tuesday’s slide into a longer-term perspective. ‘‘All who invest should feel grateful that we’ve had a great run for the last 12 to 18 months,’’ said Joel Kleinman, a Washington, D.C. attorney, adding that he has learned to not read too much into any short-term ups and downs. ‘‘This is another day in the market.’’ Still, traders’ dwindling confidence was knocked down further by data showing that the economy may be decelerating more than anticipated. A Commerce Department report that orders for durable goods in January dropped by the largest amount in three months exacerbated jitters about the direction of the U.S. economy, just a day after former Federal Reserve Chairman Alan Greenspan said the United States may be headed for a recession. ‘‘It looks more and more like the economy is a slow growth economy,’’ said Michael Strauss, chief economist at Commonfund. ‘‘Moderate economic growth is good — an abrupt stop in economic growth scares people.’’ The market had been expecting the government on Wednesday to revise its estimate of fourth-quarter GDP growth down to an annual rate of about 2.3 percent from an initial forecast of 3.5 percent, and grew increasingly nervous on Tuesday that the figure could come in even lower. The housing market, which the Street had been hoping had bottomed out, also looked far from recovery after a Standard & Poor’s index indicated that single-family home prices across the nation were flat in December. A later report from the National Association of Realtors said existing home sales climbed in January by the largest amount in two years, but the data didn’t erase housing-related concerns, as median home prices fell for a sixth straight month. But a growing feeling that Wall Street, which has had a big run-up since October, was due for a correction also played into Tuesday’s decline. ‘‘I think that the market was prepared to pull back. The constellation of issues that were worrying the market came to a head,’’ said Quincy Krosby, chief investment strategist at The Hartford. Still, the market will need to pull back further before its decline can officially be called a correction, which is considered a 10 percent decline in a bull market. Just a week ago, the Dow had reached new closing and trading highs, rising as high as 12,795.92; it’s now down 4.5 percent from that level. The Dow’s decline accelerated at a faster than normal pace during the afternoon after a computer glitch kept some trades from being immediately reflected in the index of 30 blue chip stocks. Dow Jones & Co., the media company which manages the flagship index, said the problem occurred after it was discovered computers were not properly calculating trades, prompting a switch to a backup computer. The result was a massive plunge in the average in the seconds it took Dow Jones to switch to its secondary computers. The broader Standard & Poor’s 500 index fell 50.33, or 3.47 percent, Tuesday to 1,399.04, and the tech-dominated Nasdaq composite index was off 96.65, or 3.86 percent, at 2,407.87. Both indexes have also turned negative for the year. The Russell 2000 index of smaller companies dropped 31.03, or 3.77 percent, to 792.66. A suicide bomber attack on the main U.S. military base in Afghanistan where Vice President Dick Cheney was visiting also rattled the market Tuesday. China’s stock market plummeted from record highs as investors took profits when concerns arose that the Chinese government may try to temper its ballooning economy by raising interest rates again or reducing more of the money available for lending. ‘‘Corrections usually happen because of a catalyst, and this may be it,’’ said Ed Peters, chief investment officer at PanAgora Asset Management. ‘‘The move in China was a surprise, and when a major market has a shock it ripples through the rest of the market. With all the trade that goes on with China, there tends to be a knee-jerk reaction with that kind of drop.’’ The Shanghai Composite Index tumbled 8.8 percent to close at 2,771.79, its biggest decline since it fell 8.9 percent on Feb. 18, 1997. Since Chinese share prices doubled last year as investors poured money into the market after the completion of shareholding reforms, trading in Shanghai has been very volatile. Hong Kong’s benchmark Hang Seng Index dropped 1.8 percent, and Malaysia’s Kuala Lumpur Composite Index fell 2.8 percent. Japan’s Nikkei stock average fell a more moderate 0.52 percent, but European markets were rattled — Britain’s FTSE 100 lost 2.31 percent, Germany’s DAX index dropped 2.96 percent, and France’s CAC-40 fell 3.02 percent. Bond prices shot higher as investors bought into the safe-haven Treasury market, pushing the yield on the benchmark 10-year Treasury briefly note down to 4.47 percent, its lowest level so far this year, from 4.63 percent late Monday; the yield settled at 4.52 percent. The durable goods drop raised the chance of the Federal Reserve easing interest rates later in the year — a possibility that makes the bond market an attractive place to be right now. The hope for slowing inflation could be dashed, though, if energy costs keep rising. Oil prices initially fell Tuesday on worries that Chinese demand could be dampened should its economy slow down, but later rose on escalating tensions in the Middle East. Light, sweet crude for April delivery fell 62 cents a barrel to $60.77 on the New York Mercantile Exchange. The dollar slipped against other major currencies, while gold also fell. The Dow has been climbing at a steady rate since last summer, but over the past few trading sessions, stocks began pulling back on the worry that the market is due for a correction. Data indicating a slower economy had recently been giving stocks a boost on the hopes that the Fed will lower interest rates, which could reinvigorate consumer spending and the struggling housing market. But the market may fall further before that happens, analysts said. ‘‘If in a week or two, the psychology in the U.S. market turns to the realization that we’re in a modest growth economy of 2 to 3 percent growth, that will help temper inflation pressures going forward. If that perception evolves, there’s an increase in the likelihood that the Fed will be lowering rates rather than raising rates. Structurally, it’s a development that should be good for the equity market, but it might be an event that unfolds after prices are lower,’’ Strauss said. Declining issues outnumbered advancers by about 7 to 1 on the New York Stock Exchange, where volume came to a very heavy 2.38 billion shares, compared with 1.55 billion Monday. ——— On the Net: New York Stock Exchange: http://www.nyse.com Nasdaq Stock Market: http://www.nasdaq.com

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